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  <div class="section" id="numpy-random-generator-normal">
<h1>numpy.random.Generator.normal<a class="headerlink" href="#numpy-random-generator-normal" title="Permalink to this headline">¶</a></h1>
<p>method</p>
<dl class="method">
<dt id="numpy.random.Generator.normal">
<code class="sig-prename descclassname">Generator.</code><code class="sig-name descname">normal</code><span class="sig-paren">(</span><em class="sig-param">loc=0.0</em>, <em class="sig-param">scale=1.0</em>, <em class="sig-param">size=None</em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.Generator.normal" title="Permalink to this definition">¶</a></dt>
<dd><p>Draw random samples from a normal (Gaussian) distribution.</p>
<p>The probability density function of the normal distribution, first
derived by De Moivre and 200 years later by both Gauss and Laplace
independently <a class="reference internal" href="#r1536f9c044a3-2" id="id1">[2]</a>, is often called the bell curve because of
its characteristic shape (see the example below).</p>
<p>The normal distributions occurs often in nature.  For example, it
describes the commonly occurring distribution of samples influenced
by a large number of tiny, random disturbances, each with its own
unique distribution <a class="reference internal" href="#r1536f9c044a3-2" id="id2">[2]</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>loc</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Mean (“centre”) of the distribution.</p>
</dd>
<dt><strong>scale</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Standard deviation (spread or “width”) of the distribution. Must be
non-negative.</p>
</dd>
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape.  If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn.  If size is <code class="docutils literal notranslate"><span class="pre">None</span></code> (default),
a single value is returned if <code class="docutils literal notranslate"><span class="pre">loc</span></code> and <code class="docutils literal notranslate"><span class="pre">scale</span></code> are both scalars.
Otherwise, <code class="docutils literal notranslate"><span class="pre">np.broadcast(loc,</span> <span class="pre">scale).size</span></code> samples are drawn.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>Drawn samples from the parameterized normal distribution.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.stats.norm</span></code></a></dt><dd><p>probability density function, distribution or cumulative density function, etc.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The probability density for the Gaussian distribution is</p>
<div class="math">
<p><img src="../../../_images/math/b4a4f5ca59e5559aa092b30b98184ec0bb689b7a.svg" alt="p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }}
e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} },"/></p>
</div><p>where <img class="math" src="../../../_images/math/4a3598141469c2555591e66606a1b86d4ec6dca9.svg" alt="\mu"/> is the mean and <img class="math" src="../../../_images/math/b52df27bfb0b1e3af0c2c68a7b9da459178c2a7d.svg" alt="\sigma"/> the standard
deviation. The square of the standard deviation, <img class="math" src="../../../_images/math/5406eadc281dbd20de843b0034c8497320dae5cb.svg" alt="\sigma^2"/>,
is called the variance.</p>
<p>The function has its peak at the mean, and its “spread” increases with
the standard deviation (the function reaches 0.607 times its maximum at
<img class="math" src="../../../_images/math/f7492160b86fd4af6ef77b3d8c7a87b5b579a959.svg" alt="x + \sigma"/> and <img class="math" src="../../../_images/math/cbb07bab26e93435b8b14428331f349a4632e6a6.svg" alt="x - \sigma"/> <a class="reference internal" href="#r1536f9c044a3-2" id="id3">[2]</a>).  This implies that
<a class="reference internal" href="numpy.random.normal.html#numpy.random.normal" title="numpy.random.normal"><code class="xref py py-meth docutils literal notranslate"><span class="pre">normal</span></code></a> is more likely to return samples lying close to the
mean, rather than those far away.</p>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r1536f9c044a3-1"><span class="brackets">1</span></dt>
<dd><p>Wikipedia, “Normal distribution”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Normal_distribution">https://en.wikipedia.org/wiki/Normal_distribution</a></p>
</dd>
<dt class="label" id="r1536f9c044a3-2"><span class="brackets">2</span><span class="fn-backref">(<a href="#id1">1</a>,<a href="#id2">2</a>,<a href="#id3">3</a>)</span></dt>
<dd><p>P. R. Peebles Jr., “Central Limit Theorem” in “Probability,
Random Variables and Random Signal Principles”, 4th ed., 2001,
pp. 51, 51, 125.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>Draw samples from the distribution:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mu</span><span class="p">,</span> <span class="n">sigma</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span> <span class="c1"># mean and standard deviation</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">()</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">mu</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
</pre></div>
</div>
<p>Verify the mean and the variance:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nb">abs</span><span class="p">(</span><span class="n">mu</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">s</span><span class="p">))</span>
<span class="go">0.0  # may vary</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nb">abs</span><span class="p">(</span><span class="n">sigma</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">ddof</span><span class="o">=</span><span class="mi">1</span><span class="p">))</span>
<span class="go">0.1  # may vary</span>
</pre></div>
</div>
<p>Display the histogram of the samples, along with
the probability density function:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">count</span><span class="p">,</span> <span class="n">bins</span><span class="p">,</span> <span class="n">ignored</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="p">(</span><span class="n">sigma</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span> <span class="o">*</span>
<span class="gp">... </span>               <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span> <span class="o">-</span> <span class="p">(</span><span class="n">bins</span> <span class="o">-</span> <span class="n">mu</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">sigma</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="p">),</span>
<span class="gp">... </span>         <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;r&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../../_images/numpy-random-Generator-normal-1_00_00.png" src="../../../_images/numpy-random-Generator-normal-1_00_00.png" />
</div>
<p>Two-by-four array of samples from N(3, 6.25):</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">()</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="go">array([[-4.49401501,  4.00950034, -1.81814867,  7.29718677],   # random</span>
<span class="go">       [ 0.39924804,  4.68456316,  4.99394529,  4.84057254]])  # random</span>
</pre></div>
</div>
</dd></dl>

</div>


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